Problem 2 [6+2+2=10 points]. Suppose your friend has randomly picked a number from {1, 3, 5, 7, 9, 11, 13, 15} and each number is equally likely. You have to guess the number by asking only the following type of question: "Is the number ?" where i E {1, 3, 5, 7, 9, 11, 13, 15}. Your friend can only answer yes or no to each question. (Hint: In this problem, numbers are picked without replacement.) 1) Let X denote the number of questions of the above type you need to ask until you guess the number correctly. What is the value of the following quantities? To get full marks you need to present the detail calculation and the final answers must be simplified fully. P(X = 1) P(X = 2) = EX2] = var [X] = 2) What bound on P(|X - 4.5| 2 3) is implied by the Chebyshev bound? 3) What is the exact value of P(|X - 4.5| 2 3)